Wide Scalar Neutrino Resonance andbb¯Production at the CERN Collider LEP

In supersymmetric models with $R$-parity violation, scalar neutrinos $\tilde{\nu }$ may be produced as $s$-channel resonances in $e^{+}{e}^{-}$ colliders. We note that within current constraints the scalar neutrino may have a width of several GeV into $b\overline{b}$ and be produced with large cross section, leading to a novel supersymmetry discovery signal at the CERN collider LEP II. In addition, if $m_{\tilde{\nu }}\approx m_Z$, such a resonance necessarily increases $R_b$ and reduces $A_{\mathrm{FB}}\left(b\right)$, significantly improving the fit to electroweak data. Bounds from $B$ meson and top quark decays are leading constraints, and we stress the importance of future measurements.